Fundamental solutions to elasticity problems for the lower half-plane were constructed that correspond to the action of a periodic system of concentrated forces and periodically arranged discrete boundary dislocations at internal points. The expressions for the stresses and displacements that were derived were Green's functions for the corresponding periodic problems. In particular, they were for problems which were based upon the periodically arranged cuts in the half-plane. Green's functions were also obtained that permitted the construction of solutions to basic periodic problems on a half-plane. That is, for a given periodic loading or for given periodic displacements.

Green's Functions for Periodic Problems of Elastic Half-Plane. M.A.Grekov: Mechanics of Solids, 1998, 33[3], 142-6 (Mekh. Tverdogo Tela, 1998, 33[3], 173-8)